Electric Charge And Electric Field - Pearson
Chapter 17Electric Chargeand Electric FieldIn a thundercloud, it is believed thatcollisions between ice and slush particlesgive the ice particles a slight positivecharge. Although the details of this processare not understood, the resulting chargeseparation can produce enormous electricfields that result in a lightning bolt.When you scuff your shoes across a carpet, you canget zapped by an annoying spark of static electricity.That same spark could, in principle, totally destroy anintegrated circuit chip in your computer. Fortunately, most modern electronic devices are designed to prevent such a catastrophe.Lightning, the same phenomenon on a vastly larger scale, candestroy a lot more than computer chips. All these phenomena involve electric charges and the interactions between such charges.By the end of this chapter, you will be able to:1. Sketch the distribution of charges for bothconducting and insulating objects in various arrangements.2. Calculate the number of fundamental units ofcharge in a particular quantity of charge.3. Determine both the magnitude and direction ofthe force one charge exerts on another usingCoulomb’s law.4. Determine the net force acting on a charge dueto an array of point charges.5. Relate both the magnitude and direction of theelectric field at a point to the force felt by acharge placed at that point.6. Determine the net electric field at a point due toboth an array of point charges and a symmetriccharge distribution.7. Determine the electric flux through a surface.8. Relate the net electric flux through a closedsurface to the amount of charge enclosed bythe surface.In this chapter, we’ll study how electric charges that are atrest in our frame of reference influence each other; we call theseelectrostatic interactions. We’ll find that charge has interesting properties. It is quantized: The total electric charge in a system must be an integer multiple of the charge of a single electron.Electric charge also obeys a conservation law: Charge can beneither created nor destroyed. However, most of the chapter willbe devoted to the forces that charges produce on other charges.525M17 YOUN2788 10 SE C17 525-561.indd 5259/23/14 4:59 PM
526CHAPTER 17 Electric Charge and Electric FieldThese electrostatic forces are governed by Coulomb’s law and are mediated by electricfields. Electrostatic forces hold atoms, molecules, and our bodies together, but they alsoare constantly trying to tear apart the nuclei of atoms. We’ll explore all these concepts inthis chapter.17.1 Electric ChargeThe ancient Greeks discovered as early as 600 B.C. that when they rubbed amber withwool, the amber could attract other objects. Today we say that the amber has acquired anet electric charge, or has become charged. The word electric is derived from the Greekword elektron, meaning “amber.” When you scuff your shoes across a nylon carpet, youbecome electrically charged, and you can charge a comb by passing it through dry hair.Plastic rods and fur (real or fake) are particularly good for demonstrating electric-chargeinteractions. In Figure 17.1a, we charge two plastic rods by rubbing them on a piece of fur.We find that the rods repel each other. When we rub glass rods with silk (Figure 17.1b), theglass rods also become charged and repel each other. But a charged plastic rod attracts acharged glass rod (Figure 17.1c, top). Furthermore, the plastic rod and the fur attract eachother, and the glass rod and the silk attract each other (Figure 17.1c, bottom).These experiments and many others like them have shown that there are exactly two(no more) kinds of electric charge: the kind on the plastic rod rubbed with fur and the kindon the glass rod rubbed with silk. Benjamin Franklin (1706–1790) suggested calling thesetwo kinds of charge negative and positive, respectively, and these names are still used. ApplicationRun!The person in this vacation snapshot, takenat a scenic overlook in Sequoia NationalPark, was amused to find her hair standing onend. Luckily, she and her companion left theoverlook after taking the photo—and beforeit was hit by lightning. Just before lightningstrikes, strong charges build up in the groundand in the clouds overhead. If you’re standingon charged ground, the charge will spreadonto your body. Because like charges repel,all your hairs tend to get as far from eachother as they can. But the key thing is for youto get as far from that spot as you can!Like and unlike chargesTwo positive charges or two negative charges repel each other; a positive and anegative charge attract each other.In Figure 17.1, the plastic rod and the silk have negative charge; the glass rod and the furhave positive charge.When we rub a plastic rod with fur (or a glass rod with silk), both objects acquire netcharges, and the net charges of the two objects are always equal in magnitude and oppositein sign. These experiments show that in the charging process we are not creating electricPlain plastic rods neitherattract nor repel eachother.Fur– – – – –Silk. but after beingrubbed with fur,the rods repeleach other.–The fur-rubbed plasticrod and the silkrubbed glass rodattract eachother.– – – – –Plastic–Plain glass rods neitherattract nor repel eachother.–––(a) Interaction between plastic rods rubbedon fur Glass . but after beingrubbed with silk,the rods repeleach other. (b) Interaction between glass rods rubbedon silk. and the fur and silkeach attracts the rod itrubbed. (c) Interaction between objects with oppositecharges Figure 17.1 Experiments illustrating the nature of electric charge.M17 YOUN2788 10 SE C17 525-561.indd 5269/23/14 4:59 PM
17.1 Electric Charge527charge, but transferring it from one object to another. We now know that the plastic rod acquires extra electrons, which have negative charge. These electrons are taken from the fur,which is left with a deficiency of electrons (that is, fewer electrons than positively chargedprotons) and thus a net positive charge. The total electric charge on both objects does notchange. This is an example of conservation of charge; we’ll come back to this importantprinciple later.Conceptual Analysis 17.1The sign of the chargeThree balls made of different materials are rubbed against differenttypes of fabric—silk, polyester, and others. It is found that balls 1 and 2repel each other and that balls 2 and 3 repel each other. From this result,we can conclude thatSolution Since balls 1 and 2 repel, they must be of the same sign,either both positive or both negative. Since balls 2 and 3 repel eachother, they also must be of the same sign. This means that 1 and 3 bothhave the same sign as 2, so all three balls have the same sign. The correct answer is C.A. balls 1 and 3 carry charges of opposite sign.B. balls 1 and 3 carry charges of the same sign; ball 2 carries a chargeof the opposite sign.C. all three balls carry charges of the same sign.The physical basis of electric chargeWhen all is said and done, we can’t say what electric charge is; we can only describe itsproperties and its behavior. However, we can say with certainty that electric charge is oneof the fundamental attributes of the particles of which matter is made. The interactionsresponsible for the structure and properties of atoms and molecules—and, indeed, of all ordinary matter—are primarily electrical interactions between electrically charged particles.The structure of ordinary matter can be described in terms of three particles: the negatively charged electron, the positively charged proton, and the uncharged neutron. Theprotons and neutrons in an atom make up a small, very dense core called the nucleus, witha diameter on the order of 10-15 m (Figure 17.2). Surrounding the nucleus are the electrons, which orbit the nucleus out to distances on the order of 10-10 m. If an atom were afew miles across, its nucleus would be the size of a tennis ball.The masses of the individual particles, to the precision that they are currently known,are as follows:Mass of electron m e 9.109382911402 * 10-31 kg,Mass of proton m p 1.6726217771742 * 10-27 kg,Mass of neutron m n 1.6749273511742 * 10-27 kg.The numbers in parentheses are the uncertainties in the last two digits. Note that the massesof the proton and neutron are nearly equal (within about 0.1%) and that the mass of theproton is roughly 2000 times that of the electron. Over 99.9% of the mass of any atom isconcentrated in its nucleus.The negative charge of the electron has (within experimental error) exactly the samemagnitude as the positive charge of the proton. In a neutral atom, the number of electronsequals the number of protons in the nucleus, and the net electric charge (the algebraic sumof all the charges) is exactly zero (Figure 17.3a). The number of protons or electrons inneutral atoms of any element is called the atomic number of the element.When the number of protons in an object equals the number of electrons in the object,the total charge is zero, and the object as a whole is electrically neutral. To give a neutralobject an excess negative charge, we may either add negative charges to it or remove positive charges from it. Similarly, we can give an excess positive charge to a neutral body byeither adding positive charge or removing negative charge. When we speak of the chargeon an object, we always mean its net charge.M17 YOUN2788 10 SE C17 525-561.indd 527Atom 10 -10 mMost of theatom’s volumeis occupiedsparsely byelectrons.Tiny compared with therest of the atom, thenucleus contains over99.9% of the atom’s mass.Nucleus 10 -15 mProton:Positive chargeMass 1.673 * 10 -27 kgNeutron: No chargeMass 1.675 * 10 -27 kgElectron: Negative chargeMass 9.109 * 10 -31 kgThe charges of the electron andproton are equal in magnitude. Figure 17.2 Schematic depiction of thestructure and components of an atom.9/23/14 4:59 PM
528CHAPTER 17 Electric Charge and Electric FieldProtons ( )NeutronsElectrons (-)(a) Neutral lithium atom (Li):3 protons (3 )4 neutrons3 electrons (3-)Electrons equal protons:Zero net charge(b) Positive lithium ion (Li ): (c) Negative lithium ion (Li ):3 protons (3 )3 protons (3 )4 neutrons4 neutrons2 electrons (2-)4 electrons (4-)More electrons than protons:Fewer electrons than protons:Negative net chargePositive net charge Figure 17.3 The neutral lithium (Li) atom and positive and negative lithium ions.Nonconductingnylon threads–MetalballCopperwire–Chargedplastic rod–––The wire conducts charge from the negativelycharged plastic rod to the metal ball.(a)––A negatively chargedplastic rod now repelsthe ball .– –– ––Chargedplastic rod(b). and a positivelycharged glass rodattracts the ball.–– Chargedglass rod(c) Figure 17.4 Charging by conduction.A copper wire is a good conductor. (a) Thewire conducts charge between the plasticrod and the metal ball, giving the ball anegative charge. The charged ball is then(b) repelled by a like charge and (c) attractedby an unlike charge.M17 YOUN2788 10 SE C17 525-561.indd 528An ion is an atom that has lost or gained one or more electrons. If one or more electrons areremoved, the remaining positively charged structure is called a positive ion (Figure 17.3b). Anegative ion is an atom that has gained one or more electrons (Figure 17.3c). This gaining orlosing of electrons is called ionization.Ordinarily, when an ion is formed, the structure of the nucleus is unchanged. In a solidobject such as a carpet or a copper wire, the nuclei of the atoms are not free to move about,so a net charge is due to an excess or deficit of electrons. However, in a liquid or a gas, anet electric charge may be due to movements of ions. Thus, a positively charged region in afluid could represent an excess of positive ions, a deficit of negative ions, or both.17.2 Conductors and InsulatorsSome materials permit electric charge to move from one region of the material to another;others do not. For example, Figure 17.4 shows a copper wire supported by a nylon thread.Suppose you touch one end of the wire to a charged plastic rod and touch the other end to ametal ball that is initially uncharged. When you remove the copper wire and bring anothercharged object near the ball, the ball is attracted or repelled, showing that it has becomeelectrically charged. Electric charge has been transferred through the copper wire betweenthe ball and the surface of the plastic rod.The wire is called a conductor of electricity. If you repeat the experiment, but thistime using a rubber band or nylon thread in place of the wire, you find that no charge istransferred to the ball. These materials are called insulators. Conductors permit chargeto move through them; insulators do not. Carpet fibers on a dry day are good insulatorsand allow charge to build up on us as we walk across the carpet. Coating the fibers withan antistatic layer that does not easily transfer electrons to or from our shoes is onesolution to the charge-buildup problem; another is to wind some of the fibers aroundconducting cores.Most of the materials we call metals are good conductors, and most nonmetals are insulators. Within a solid metal such as copper, one or more outer electrons in each atombecome detached and can move freely throughout the material, just as the molecules of agas can move through the spaces between the grains in a bucket of sand. The other electrons remain bound to the positively charged nuclei, which themselves are bound in fixedpositions within the material. In an insulator, there are no, or at most very few, free electrons, and electric charge cannot move freely through the material.Some materials called semiconductors are intermediate in their properties betweengood conductors and good insulators. Unlike copper, which is always a good conductor, nomatter what you do to it, or rubber, which is always a bad conductor, no matter what you doto it, a semiconductor such as silicon can be engineered to have a controllable conductivity.9/23/14 4:59 PM
17.2 Conductors and Insulators529This is the basis of the silicon-based transistor, which is the fundamental building block ofthe modern computer.Finally, we note that, in a liquid or gas, charge can move in the form of positive ornegative ions. Ionic solutions are usually good conductors. For example, when ordinarytable salt (NaCl) dissolves in water, each sodium (Na) atom loses an electron to becomea positively charged sodium ion 1Na 2, and each chlorine 1Cl2 atom gains an electron tobecome a negatively charged chloride ion 1Cl-2. These charged particles can move freelyin the solution and thus conduct charge from one region of the fluid to another, providinga mechanism for conductivity. Ionic solutions are the dominant conductivity mechanism inmany biological processes.InductionWhen we charge a metal ball by touching it with an electrically charged plastic rod, someof the excess electrons on the rod move from it to the ball, leaving the rod with a smallernegative charge. In another technique, called charging by induction, the plastic rod cangive another object a charge of opposite sign without losing any of its own charge.Figure 17.5 shows an example of charging by induction. A metal sphere is supportedon an insulating stand (step 1). When you bring a negatively charged rod near the sphere,without actually touching it (step 2), the free electrons on the surface of the sphere arerepelled by the excess electrons on the rod, and they shift toward the right, away from therod. They cannot escape from the sphere because the supporting stand and the surroundingair are insulators. As a result, negative charge accumulates on the right side of the surfaceof the sphere and positive charge (due to the positive nuclei that the electrons left behind)accumulates on the left side. These excess charges are called induced charges.Not all of the free electrons move to the right side of the surface of the sphere. As soonas any induced charge develops, it exerts forces toward the left on the other free electrons.These electrons are repelled from the negative induced charge on the right and attractedtoward the positive induced charge on the left. The system reaches an equilibrium state inwhich the force toward the right on an electron, due to the charged rod, is just balanced bythe force toward the left, due to the induced charge. If we remove the charged rod, the freeelectrons shift back to the left, and the original neutral condition is restored.What happens if, while the plastic rod is nearby, you touch one end of a conductingwire to the right surface of the sphere and the other end to the earth (step 3 in Figure 17.5)?The earth is a conductor, and it is so large that it can act as a practically infinite source ofextra electrons or sink of unwanted electrons. Some of the negative charge flows throughthe wire to the earth. Now suppose you disconnect the wire (step 4) and then remove therod (step 5); a net positive charge is left on the sphere. The charge on the negatively chargedrod has not changed during this process. The earth acquires a negative charge that is equalin magnitude to the induced positive charge remaining on the sphere.Charging by induction would work just as well if the mobile charges in the sphere werepositive charges instead of (negatively charged) electrons or even if both positive and negative mobile charges were present (as would be the case if we replaced the sphere with a flaskof salt water). In this book, we’ll talk mostly about metallic conductors, in which the mobileInsulatingstand1 Uncharged metal ballElectronElectrondeficiencybuildup –Negativelycharged – – –rod – –––Metalball2 Negative charge on rodrepels electrons, creatingzones of negative andpositive induced charge.–––– ––––WireGround3 Wire lets electron buildup(induced negative charge)flow into ground.––––– ApplicationGood conductor, bad conductor.Salt water is salty because it contains anabundance of dissolved ions. These ions arecharged and can move freely, so salt wateris an excellent conductor of electricity.Ordinary tap water contains enough ions toconduct electricity reasonably well—which iswhy you should never, ever, use an electrical device in a bathtub. However, absolutelypure distilled water is an insulator because itconsists of only neutral water molecules. – Negativecharge inground––––––4 Wire removed; ball now5 Rod removed; positivehas only an electrondeficient region ofpositive charge.charge spreads overball. Figure 17.5 Charging a metal ball by induction.M17 YOUN2788 10 SE C17 525-561.indd 5299/23/14 4:59 PM
530CHAPTER 17 Electric Charge and Electric FieldBall withpositive chargeMetal ballwith induced charges – A –B uu Fpull – Fpush Ball A’s ( ) charge pulls on the(–) induced charge and pushes onthe ( ) induced charge. Because the(–) charge is closer to A, thepull is stronger than the push,so B is attracted to A. Figure 17.7 The charge on ball Ainduces charges in ball B, resulting in a netattractive force between the balls.PhET: Balloons and Static ElectricityNegativelychargedcombThecomb’s (–)charge repelsuFthe electrons inueach molecule in Fthe paper, creatinginduced charges. Theside of the paper facingthe comb thus has a slightnet positive charge.Molecules withinduced charges – – – – – – – – – – – –Paper scrap(insulator)Positivelychargedcomb – – –– – – – – – – – – – –uFu FA comb with a ( )charge also createsinduced charges that attractthe paper to the comb. Figure 17.8 A charged comb picks upuncharged paper by polarizing the paper’smolecules. Figure 17.6 A charged plastic comb picks up unchargedbits of paper.charges are negative electrons. However, even in a metal, we can describe conduction asthough the moving charges were positive. In terms of transfer of charge in a conductor, amovement of electrons to the left is exactly equivalent to a movement of imaginary positiveparticles to the right. In fact, when we study electric currents, we will find that, for historicalreasons, currents in wires are described as though the moving charges were positive.When excess charge is placed on a solid conductor and is at rest (i.e., an electrostaticsituation), the excess charge rests entirely on the surface of the conductor. If there wereexcess charge in the interior of the conductor, there would be electric forces among theexcess charges that would cause them to move, and the situation couldn’t be electrostatic.PolarizationA charged object can exert forces even on objects that are not charged themselves. If you ruba balloon on a rug and then hold the balloon against the ceiling, it sticks, even though theceiling has no net electric charge. After you electrify a comb by running it through your hair,you can pick up uncharged bits of paper on the comb (Figure 17.6). How is this possible?The interaction between the balloon and the ceiling or between the comb and the paperis an induced-charge effect. In step 2 of Figure 17.5, the plastic rod exerts a net attractive force on the sphere, even though the total charge on the sphere is zero, because thepositive charges are closer to the rod than the negative charges are. Figure 17.7 shows thiseffect more clearly. The large ball A has a positive charge; the conducting metal ball B isuncharged. When we bring B close to A, the positive charge on A pulls on the electrons inB, setting up induced charges. Because the negative induced charge on the surface of B iscloser to A than the positive induced charge is, A exerts a net attraction on B. (We’ll studythe dependence of electric forces on distance in Section 17.4.) Even in an insulator, theelectric charges can shift back and forth a little when there is charge nearby. Figure 17.8shows how a static charge enables a charged plastic comb to pick up uncharged bits ofpaper. Although the electrons in the paper are bound to their molecules and cannot movefreely through the paper, they can still shift slightly to produce a net charge on one sideand the opposite charge on the other. Thus, the comb causes each molecule in the paper todevelop induced charges (an effect called polarization). The net result is that the scrap ofpaper shows a slight induced charge—enough to enable the comb to pick it up.17.3 Conservation and Quantization of ChargeVideo Tutor DemoM17 YOUN2788 10 SE C17 525-561.indd 530As we’ve discussed, an electrically neutral object is an object that has equal numbers ofelectrons and protons. The object can be given a charge by adding or removing either positive or negative charges. Implicit in this discussion are two very important principles. Firstis the principle of conservation of charge:9/23/14 4:59 PM
17.4 Coulomb’s Law531Conservation of chargeThe algebraic sum of all the electric charges in any closed system is constant. Chargecan be neither created nor destroyed; it can only move from one place or object toanother.Conservation of charge is believed to be a universal conservation law; there has neverbeen any experimental evidence for a violation of this principle. Even in high-energy interactions in which subatomic particles are created and destroyed, the net charge of all theparticles is exactly constant.Second, the magnitude of the charge of the electron or proton is a natural unit of charge.Every amount of observable electric charge is always an integer multiple of this basic unit.Hence we say that charge is quantized. A more familiar example of quantization is money.When you pay cash for an item in a store, you have to do it in 1-cent increments. If grapefruits are selling three for a dollar, you can’t buy one for 3313 cents; you have to pay 34cents. Cash can’t be divided into smaller amounts than 1 cent, and electric charge can’t bedivided into smaller amounts than the charge of one electron or proton.Quantitative Analysis 17.1Determine the chargeSolution When identical metal objects come in contact, any netThree identical metal balls A, B, and C are mounted on insulating rods.Ball A has a charge q, and balls B and C are initially uncharged (q isthe usual symbol for electric charge). Ball A is touched first to ball Band then separately to ball C. At the end of this experiment, the chargeon ball A isA. q 2.B. q 3.charge they carry is shared equally between them. Thus, when A touches B, each ends up with a charge q 2. When A then touches C, thischarge is shared equally, leaving A and C each with a charge of q 4.The correct answer is C.C. q 4.The forces that hold atoms and molecules together are fundamentally electrical inn ature. The attraction between electrons and protons holds the electrons in atoms, holds atoms together to form polyatomic molecules, holds molecules together to form solids orliquids, and accounts for phenomena such as surface tension and the stickiness of glue.Within the atom, the electrons repel each other, but they are held in the atom by the attractiveforce of the protons in the nucleus. But what keeps the positively charged protons togetherin the tiny nucleus despite their mutual repulsion? They are held by another, even strongerinteraction called the nuclear force. (We will learn about the nuclear force in Chapter 30.)17.4 Coulomb’s LawCharles Augustin de Coulomb (1736–1806) studied the forces between charged particles indetail in 1784 using a torsion balance. The torsion balance, which is depicted in Figure 17.9a,consisted of a small rod that was suspended from its midpoint by a fine wire. On each end ofthe rod was a charged sphere. When Coulomb brought a third charged sphere near one of theends of the rod, it caused the rod to rotate slightly about its center of mass. By measuring thedirection and magnitude of the angular deflection, Coulomb was able to deduce some of thebasic properties of the electric force between charges. This very sensitive technique would B IO Application Static cling.The genetic code is carried by the “double helix” of DNA, which consists of two DNA strands woundaround each other. The two strands stick together by what is essentially static cling. Along each strand,specific molecular groups form dipoles, with a positive or negative end projecting outward. The positivecharges on one strand interact precisely with the negative charges on the other, “zipping” the two strandstogether. Crucially, these interactions are strong enough to keep the strands from coming apart on theirown, but weak enough that the cellular machinery can “unzip” the strands for copying.M17 YOUN2788 10 SE C17 525-561.indd 5319/23/14 4:59 PM
532CHAPTER 17 Electric Charge and Electric FieldThe negativelycharged ball attractsthe positively chargedone; the positive ballmoves until the elasticforces in the torsionfiber balance theelectrostatic attraction.Torsion fiberChargedpith balls – Scalebe used 13 years later by Cavendish to study the (much weaker) gravitational force betweenlead spheres, as we discussed in Section 6.3. Coulomb’s experiments led to the very important discovery that the electric force between two point charges (charged bodies that are verysmall in comparison with the distance r between them) is proportional to the inverse squareof the distance between the charges, 1 r 2.The force also depends on the quantity of charge on each object, which we’ll denote byq or Q. To explore this dependence, Coulomb divided a charge into two equal parts by placing a small charged spherical conductor in contact with an identical but uncharged sphere;by symmetry, the charge is shared equally between the two spheres. (Note the essential roleof the principle of conservation of charge in this procedure.) Thus, Coulomb could obtainone-half, one-quarter, and so on, of any initial charge. He found that the forces that twopoint charges q1 and q2 exert on each other are proportional to each charge and thereforeare proportional to the product q1q2 of the two charges.Coulomb’s law(a) A torsion balance of the type used byCoulomb to measure the electric forceuF2 on 1r Like charges repel.q1uuuF1 on 2 1-F2 on 12.F1 on 2 F2 on 1 kq1q2F1 on 20 q1q2 0r2r Unlike charges attract.uF2 on 1uF1 on 2The magnitude F of the force that each of two point charges q1 and q2 a distance rapart exerts on the other (Figure 17.9b) is directly proportional to the product of thecharges and inversely proportional to the square of the distance between them. Therelationship is expressed symbolically asF k q1 q2 r2.(17.1)This relationship is called Coulomb’s law.Units: q1 and q2 are in coulombs (C); F is in newtons (N).Notes: k is a fundamental constant of nature: k 8.987551789 * 109 N # m2 C2. F represents only the magnitude of the force; the direction is determined using the factthat like charges repel and unlike charges attract. r is the distance between the two charges.q2(b) Interaction of like and unlike charges Figure 17.9 Schematic depiction of theapparatus Coulomb used to determine theforces between charged objects that can betreated as point charges.M17 YOUN2788 10 SE C17 525-561.indd 532The SI unit of electric charge is called one coulomb (1 C). For numerical calculationsin problems, we’ll often use the approximate valuek 8.99 * 109 N#m2 C2,which is in error by about 0.03%.The forces that two charges exert on each other always act along the line joining thecharges. The two forces are always equal in magnitude and opposite in direction, evenwhen the charges are not equal. The forces obey Newton’s third law.As we’ve seen, q1 and q2 can be either positive or negative quantities. When the chargeshave the same sign (both positive or both negative), the forces are repulsive; when they areunlike, the forces are attractive. We need the absolute value bars in Equation 17.1 becauseF is the magnitude of a vector quantity. By definition, F is always positive, but the productq1 q2 is negative whenever the two charges have opposite signs.The proportionality of the electric force to 1 r 2 has been verified with
528 CHAPTER 17 Electric Charge and Electric Field An ion is an atom that has lost or gained one or more electrons. If one or more electrons are removed, the remaining positively charged structure is called a positive ion (Figure 17.3b). A negative ion is an atom that has gained one or more electrons (Figure 17.3c).
20.1 Electric Charge and Static Electricity The effect an electric charge has on other charges in the space around it is the charge’s electric field. An electric field exerts forces on any charged object placed in the field
The Princeton Review Practice SAT Physics Subject Test 1 431 GO ON TO THE NEXT PAGE 27. Four point charges are labeled Charge 1, Charge 2, Charge 3, and Charge 4. It is known that Charge 1 attracts Charge 2, Charge 2 repels Charge 3, and Charge 3 attracts Charge 4. Which
F K q 1q 2/r2 (Coulomb's Law) where K depends on the system of units K 8.99x10 9 Nm 2/C 2 (in MKS system) K 1/(4 πε0) where ε0 8.85x10-12 C 2/(Nm 2) Electric Charge : electron charge -e e 1.6x10-19 C proton charge e C Coulomb Electric charge is a conserved quantity (net electric charge is never created or destroyed !) q 1 q 2 r
16.8 Field Lines The electric field between two closely spaced, oppositely charged parallel plates is constant. 16.8 Field Lines Summary of field lines: 1. Field lines indicate the direction of the field; the field is tangent to the line. 2. Th
Charge q C Linear charge density l C/m Surface charge density s C/m2 Volume charge density r C/m3 Table 22-2 Fig. 22-10 A ring of uniform positive charge.A differential element of charge occupies a length ds (greatly exaggerated for clarity).This element sets up an electric Þeld at point P.T
Electric field, q 0 is a positive test charge; F is electrostatic force that acts on the test chargethe test charge 7. FqE , Electrostatic force that acts on the particle with charge q. 8. E 22 0 1 4 qq rk r rr , Electric field due to Point charge 1 9. 33 00 11 22 qd p E zz , Electric field
Electric Fields (page 602) 8. A charge’s electric field is the effect the charge has on in the space around it. 9. Circle the letters of the factors that the strength of an electric field depends on. a.the direction of the field b.whether the charge is positive or negative c.the amount of charge that produc
The electric field is stronger where the field lines are closer together. 16.8 Field Lines Electric dipole: two equal charges, opposite in sign: 16.8 Field Lines The electric field between two closely spaced, oppositely charg
